Journal of University of Chinese Academy of Sciences >
A homogeneous infeasible-interior-point algorithm for semidefinite programming
Received date: 2015-03-18
Revised date: 2015-09-15
Online published: 2016-05-15
We propose a homogeneous infeasible-interior-point algorithm for semidefinite programming(SDP) in a new wide neighborhood in order to achieve low iteration complexity and get better experiement numerical results. Complementarity problem (MCP) is the KKT condition of SDP. We sovle MCP by constructing a homogeneous MCP model (HMCP) and proposing a new wide neighborhood. Then we derive the optimal solution of SDP. This algorithm can be easily used to determine whether SDP is feasible or not. At the direction of NT, we prove that the iteration poin is convergent in new wide neighborhood and the iteration complexity is O(√nlogL), where n is the dimension of SDP and L=Tr(X0S0)/ε with ε being the required precision and (X0,S0) the initial point. This algorithm has lower complexity degree than other algorithms for SDP. The numerical experiment is provided. We have proved that this algorithm is better than other infeasible-interior-point algorithms in numerical experimentel results.
WU Yue , LIU Hongwei , XIE Di . A homogeneous infeasible-interior-point algorithm for semidefinite programming[J]. Journal of University of Chinese Academy of Sciences, 2016 , 33(3) : 317 -328 . DOI: 10.7523/j.issn.2095-6134.2016.03.006
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